Precision-resolution constrained coding scheme

Abstract

A coding scheme for data is presented in which data is encoded and decoded such that a sequence of unconstrained input binary symbols, such as 1's and 0's, is encoded into a representation according to an alphabet comprising allowable time intervals between adjacent input binary symbols according to a precision parameter p, a minimum resolution parameter α, and resolution restriction functions L(t) and R(t), thereby defining a precision-resolution (PR) constrained code, and is modulated into an output signal comprising a waveform having signal peaks corresponding to the representation and separated according to the PR-constrained code for transmission of the output signal over the data channel. In this discussion, the minimum resolution parameter is denoted as a and is not limited to integer values.

1. A method of processing data for transmission over a data channel, the method comprising:
 encoding data comprising an unconstrained sequence of input binary symbols into a representation according to an alphabet comprising allowable time intervals between adjacent input binary symbols according to a precision parameter p, a minimum resolution parameter α, and resolution restriction functions L(t) and R(t), thereby defining a precision-resolution (PR) constrained code; 
 modulating an output signal comprising a waveform having signal peaks corresponding to the representation and separated according to the PR-constrained code for transmission of the output signal over the data channel. 
 
   
   
     2. The method in  claim 1 , wherein the resolution restriction functions are specified by a multiplicative error function given by a resolution factor θ that is specified in accordance with a clock drift parameter δ where 0<δ<1, and θ is defined by θ=(1+δ)/(1−δ) and indicates a minimum disjoint neighborhood between adjacent symbols for the data channel. 
   
   
     3. The method in  claim 1 , wherein the resolution restriction functions are specified in accordance with an additive error parameter Δ. 
   
   
     4. The method in  claim 1 , wherein the precision parameter p is defined by p>1. 
   
   
     5. The method in  claim 1 , wherein the output signal waveform is produced in accordance with an increased precision value p′ that is greater than the precision parameter p specified for the data channel. 
   
   
     6. The method in  claim 1 , wherein the precision parameter p is defined by an increased precision value approaching a theoretical limit of p=∞. 
   
   
     7. The method in  claim 1 , wherein the representation of the input binary symbols is produced in accordance with an enlarged alphabet having an additional degree of freedom in attributes as compared with the representation alphabet. 
   
   
     8. The method in  claim 7 , wherein the additional degree of freedom comprises color. 
   
   
     9. The method in  claim 1 , further comprising:
 detecting a modulated waveform having signal peaks that are separated according to the PR-constrained code and quantizing time intervals between the signal peaks so as to produce a representation in accordance with the representation alphabet; and 
 decoding the representation and producing the unconstrained sequence of input binary symbols. 
 
   
   
     10. The method in  claim 9 , wherein modulating the output signal is performed by a modulator that transmits the modulated waveform over the data channel, and a detector receives the modulated waveform and performs the detecting. 
   
   
     11. The method in  claim 1 , wherein the representation alphabet includes attributes comprising color. 
   
   
     12. The method in  claim 1 , wherein the representation alphabet includes non-consecutive integers. 
   
   
     13. The method in  claim 1 , wherein the representation alphabet includes non-integer numbers. 
   
   
     14. A method of processing data received over a data channel, the method comprising:
 detecting time intervals between signal peaks of a modulated waveform and quantizing the time intervals so as to produce a quantized representation in accordance with an alphabet comprising allowable time intervals between adjacent input binary symbols according to a precision parameter p, a minimum resolution parameter α, and resolution restriction functions L(t) and R(t), thereby defining a precision-resolution (PR) constrained code; 
 decoding the quantized representation so as to produce a decoded sequence of unconstrained output binary symbols. 
 
   
   
     15. The method in  claim 14 , wherein the resolution restriction functions are specified by a multiplicative error function given by a resolution factor θ that is specified in accordance with a clock drift parameter δ where 0<δ<1, and θ is defined by θ=(1+δ)/(1−δ) and indicates a minimum disjoint neighborhood between adjacent symbols for the data channel. 
   
   
     16. The method in  claim 14 , the resolution restriction functions are specified in accordance with an additive error parameter Δ. 
   
   
     17. The method in  claim 14 , wherein the precision parameter p is defined by p>1. 
   
   
     18. The method in  claim 14 , wherein the output signal waveform is modulated in accordance with an increased precision value p′ that is greater than the precision parameter p specified for the data channel. 
   
   
     19. The method in  claim 14 , wherein the precision parameter p is defined by an increased precision value approaching a theoretical limit of p=∞. 
   
   
     20. The method in  claim 14 , wherein the quantized representation of the input binary symbols is produced in accordance with a larger alphabet having an additional degree of freedom in attributes as compared with the input binary symbols. 
   
   
     21. The method in  claim 20 , wherein the additional degree of freedom comprises color. 
   
   
     22. The method in  claim 14 , wherein the representation alphabet includes non-consecutive integers. 
   
   
     23. The method in  claim 14 , wherein the representation alphabet includes non-integer numbers. 
   
   
     24. A data device comprising:
 a processor; and 
 a data transfer interface adapted to transfer data to and from a data channel; 
 wherein the processor controls the transfer of data across the data transfer interface so the data device encodes an unconstrained sequence of input binary symbols into a representation according to an alphabet comprising allowable time intervals between adjacent input binary symbols according to a precision parameter p, a minimum resolution parameter α, and resolution restriction functions L(t) and R(t), thereby defining a precision-resolution (PR) constrained code, and modulates an output signal comprising a waveform having signal peaks corresponding to the representation and separated according to the PR-constrained code for transmission of the output signal over the data channel. 
 
   
   
     25. The data device in  claim 24 , wherein the resolution restriction functions are specified by a multiplicative error function given by a resolution factor θ that is specified in accordance with a clock drift parameter δ where 0<δ<1, and θ is defined by θ=(1+δ)/(1−δ) and indicates a minimum disjoint neighborhood between adjacent symbols for the data channel. 
   
   
     26. The data device in  claim 24 , wherein the resolution restriction functions are specified in accordance with an additive error parameter Δ. 
   
   
     27. The data device in  claim 24 , wherein the precision parameter p is defined by p>1. 
   
   
     28. The data device in  claim 24 , wherein the output signal waveform is produced in accordance with an increased precision value p′ that is greater than the precision parameter p specified for the data channel. 
   
   
     29. The data device in  claim 24 , wherein the precision parameter p is defined by an increased precision value approaching a theoretical limit of p=∞. 
   
   
     30. The data device in  claim 24 , wherein the representation of the input binary symbols is produced in accordance with an enlarged alphabet having an additional degree of freedom in attributes as compared with the representation alphabet. 
   
   
     31. The data device in  claim 24 , wherein the additional degree of freedom comprises color. 
   
   
     32. The data device in  claim 24 , wherein the processor further detects a modulated waveform having signal peaks that are separated according to the PR-constrained code and quantizing time intervals between the signal peaks so as to produce a representation in accordance with the representation alphabet and decodes the representation and produces the unconstrained sequence of input binary symbols. 
   
   
     33. The data device in  claim 32 , wherein a modulator modulates the output signal and transmits the modulated waveform over the data channel, and a detector receives the modulated waveform and performs the detecting. 
   
   
     34. The data device in  claim 24 , wherein the representation alphabet includes attributes comprising color. 
   
   
     35. The data device in  claim 24 , wherein the representation alphabet includes non-consecutive integers. 
   
   
     36. The data device in  claim 24 , wherein the representation alphabet includes non-integer numbers. 
   
   
     37. A system comprising:
 a data encoder; 
 a transmitter/modulator; 
 a receiver/detector; and 
 a data decoder; 
 wherein the data encoder encodes an unconstrained sequence of input binary symbols into a representation according to an alphabet comprising allowable time intervals between adjacent input binary symbols according to a precision parameter p, a minimum resolution parameter α, and resolution restriction functions L(t) and R(t), thereby defining a precision-resolution (PR) constrained code; 
 wherein the transmitter/modulator modulates an output signal comprising a waveform having signal peaks corresponding to the representation and separated according to the PR-constrained code for transmission of the output signal over the data channel; and 
 wherein the receiver/detector detects a modulated waveform having signal peaks that are separated according to the PR-constrained code and quantizes time intervals between the signal peaks so as to produce a representation in accordance with the representation alphabet; and 
 wherein the decoder decodes the representation and produces the unconstrained sequence of input binary symbols. 
 
   
   
     38. The system in  claim 37 , wherein the resolution restriction functions are specified by a multiplicative error function given by a resolution factor θ that is specified in accordance with a clock drift parameter δ where 0<δ<1, and θ is defined by θ=(1+δ)/(1−δ) and indicates a minimum disjoint neighborhood between adjacent symbols for the data channel. 
   
   
     39. The system in  claim 37 , wherein the resolution restriction functions are specified in accordance with an additive error parameter Δ. 
   
   
     40. A system comprising:
 a processor; and 
 program data storage containing machine executable instructions comprising a set of processing rules that are performed by the processor to implement a data encoder that processes unconstrained data comprising a sequence of data bits and maps the unconstrained data onto a modulation coding scheme for encoding data comprising an unconstrained sequence of input binary symbols into a representation according to an alphabet comprising allowable time intervals between adjacent input binary symbols according to a precision parameters, a minimum resolution parameter α, and resolution restriction functions L(t) and R(t), thereby defining a precision-resolution (PR) constrained code, and modulating an output signal comprising a waveform having signal peaks corresponding to the representation and separated according to the PR-constrained code for transmission of the output signal over the data channel, and wherein the data storage further contains a set of processing rules performed by the processor to implement a data decoder that processes constrained data and detects a modulated waveform having signal peaks that are separated according to the PR-constrained code and quantizing time intervals between the signal peaks so as to produce a representation in accordance with the representation alphabet; and decodes the representation and producing the unconstrained sequence of input binary symbols. 
 
   
   
     41. A system comprising:
 a processor; and 
 data storage containing machine executable instructions comprising a set of processing rules that are performed by the processor to implement a precision resolution (PR) coding scheme, wherein the executable instructions cause the processor to perform operations comprising:
 receiving channel specification parameters comprising transmitter precision parameter p and receiver resolution parameter α for transmission over a data channel in accordance with a target channel capacity and resolution restriction functions L(t) and R(t); 
 producing combinations of precision and resolution specifications to achieve the target channel capacity; 
 determining a set of allowable time intervals between modulation peaks for a set of data channel symbols; 
 determining a translation scheme for encoding and decoding of binary symbols for transmission over the data channel. 
 
 
   
   
     42. The system in  claim 41 , wherein the resolution restriction functions L(t) and R(t) are specified by a multiplicative error function given by a resolution factor θ that is specified in accordance with a clock drift parameter δ where 0<δ<1, and θ is defined by θ=(1+δ)/(1−δ) and indicates a minimum disjoint neighborhood between adjacent symbols for the data channel. 
   
   
     43. The system in  claim 42 , wherein the executable instructions cause the processor to determine allowable time intervals comprising an alphabet for representation of input binary symbols by adding a minimal symbol t∈R such that t is correctly aligned according to the precision parameter p, is greater than the minimal resolution parameter α, and the function set (L(t), R(t)) has an empty intersection with (L(t), R(t)) for any t′ of any previously selected alphabet symbols. 
   
   
     44. The system in  claim 41 , wherein the resolution restriction functions are specified in accordance with an additive error parameter Δ.